A soft sensor for oxide scales on the steam side of superheater tubes of utility boiler under uneven circumferential loading is proposed for the first time. First finite volume method is employed to simulate oxide scales growth temperature on the steam side of superheater tube. Then appropriate time and spatial intervals are selected to calculate oxide scales thickness along the circumferential direction. On the basis of the oxide scale thickness, the stress of oxide scales is calculated by the finite element method. At last, the oxide scale thickness and stress sensors are established on support vector machine (SMV) optimized by particle swarm optimization (PSO) with time and circumferential angles as inputs and oxide scale thickness and stress as outputs. Temperature and stress calculation methods are validated by the operation data and experimental data, respectively. The soft sensor is applied to the superheater tubes of some power plant. Results show that the soft sensor can give enough accurate results for oxide scale thickness and stress in reasonable time. The forecasting model provides a convenient way for the research of the oxide scale failure.
Oxide scale formed on the steam side of superheaters and reheaters of utility boilers in power plant brings many problems like tube clogging, overheating, and erosion of turbine blade [
As the load along the circumferential direction of the superheater tube is uneven, the oxide growth temperature is different circumferentially and so is the thickness of the oxide scales. Sabau et al. [
Support vector machine (SVM) introduced by Vapnik is a useful tool for data mining, especially in the fields of pattern recognition and regression. During the past few years, its solid theoretical foundation and good behaviors have attracted a number of researchers [
PSO is an evolutionary computation technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking. It is getting more and more attention as it is simple, fast, and easy to implement [
It is not convenient to get oxide scales thickness and stress values through theoretical method, experimental method, and simulation method for online application. In this paper, a soft sensor for oxide scales based on SVM optimized by PSO is proposed. The rest of the paper is organized as follow. Section
The model area is divided into four regions, that is, steam region, scale region, steel region, and gas region from inside to outside, as shown in Figure
Geometric model.
Cross section
Longitudinal section
The steam is fully developed turbulent flow and convection coefficient between steam and oxide scale is expressed as
Heat transfer between gas and steel is forced convection and convection coefficient is given as
The temperature can be solved by the following equation [
Oxide scale thickness is the basis of the calculation of stress. For the case where protective oxide scale is formed, the rate of scale growth is controlled by diffusion of ions through the oxide, and the growth of the oxide scales can be described by [
Take the temperature between the tube and oxide scales as the growth temperature. The growth temperature changes with the thickness of the oxide scales, so the thickness of the oxide scales should be calculated through [
The stress in oxide scales mainly consists of thermal stress, which can be calculated by the following equations [
The displacement and stress of tube and oxide scales are calculated according to mechanics of elasticity as follows:
The inlet gas temperature and steam temperature are given. The radial boundary stress of the gas side and steam side equals the gas pressure and steam pressure, respectively. The radial stress and temperature are continuous at the interface of tube and oxide scales and the interfaces of different oxide layers.
Though the stresses can be calculated by simulation method, it is time consuming. Operators are eager to monitor the oxide thickness and stress online. So a soft sensor is proposed.
Train samples of SVM are
The learning process is converted into an optimization problem according to structural risk minimization principle:
Linear insensitive loss function is defined with
Due to the sparsity, only some samples’ coefficients are not 0 in quadratic programming (
In PSO, each feasible solution of the optimization problem is seen as a “particle” of the solution space. Each particle searches the solution space following the optimal particle of the whole group. Suppose the group searches in a
In this paper, support vector machine parameters are optimized by PSO. Each particle represents a potential set of
Initialize PSO and iterate to get proper set of
Traditional methods like theoretical method, experimental method, and simulation method cannot provide accurate enough oxide scale thickness and stress in reasonable time. With the development of intelligent algorithms, the soft sensor can be qualified to do this work. In our study, SVM is employed to predict oxide scale thickness and stress.
(
Soft sensor for oxide scale thickness and stress.
Soft sensor for oxide scale thickness
Soft sensor for oxide scale stress
(
The steps of constructing the soft sensors are detailed as follows.
Collect calculation parameters of oxide scales and superheater tubes.
Program thermal calculation procedure according to 73 boiler thermal calculation standards to get the convection coefficient between steam and oxide scales and convection coefficient between gas and substrate and steam temperature and gas temperature.
Divide operating time and spatial space into several intervals reasonably considering computational cost and accuracy of the results.
Calculate the temperature distribution by finite volume method with the boundaries got in Step
Calculate the oxide scale thickness according to (
Calculate the stress of oxide scales according to (
Optimize SVM parameters for the oxide scale thickness soft sensor and stress soft sensor with leave-one-out method.
Construct thickness soft sensor and stress soft sensor with the data collecting from Steps
Two reheater tube samples of power plant in site are taken for validation [
The estimated scale thickness and the actual data.
The average internal stress of oxides on AISI 441 is measured by Raman spectroscopy in [
The physical parameters of oxide scales and superheater material are listed in Tables
The main parameters for oxide scales [
Name | Elasticity modulus/×1011 [Pa] | The Poisson ration |
---|---|---|
Fe-Cr-spinel | 2.3 | 0.31 |
Magnetite | 2.1 | 0.29 |
Hematite | 2.2 | 0.19 |
The parameters of TP347 [
Temperature [°C] | Elasticity modulus ×1011 [Pa] | The linear expansion coefficient ×10−6 [K−1] | The Poisson | Conduction coefficient [W/(m·K)] | Arrhenius constant |
Activation energy [KJ/mole] |
---|---|---|---|---|---|---|
25 | 2 | 15.27 | 0.3 | 23.2 | 5 × 109 | −171 |
100 | 1.96 | 17.3 | 0.3 | 23.2 | 5 × 109 | −171 |
200 | 1.88 | 17.5 | 0.3 | 23.2 | 5 × 109 | −171 |
300 | 1.81 | 17.7 | 0.3 | 23.2 | 5 × 109 | −171 |
400 | 1.72 | 18.2 | 0.3 | 23.2 | 5 × 109 | −171 |
500 | 1.63 | 18.6 | 0.3 | 23.2 | 5 × 109 | −171 |
600 | 1.56 | 18.9 | 0.3 | 23.2 | 5 × 109 | −171 |
Geometrical parameters.
Inner diameter [mm] | Outer diameter [mm] | Axial length [mm] | Length of gas area [mm] | Width of gas area [mm] | Operating time [h] |
---|---|---|---|---|---|
36.7 | 44.5 | 15 | 1000 | 500 | 10000 |
Boundary conditions.
Inlet temperature [°C] | Inlet velocity [m/s] | Outlet pressure [MPa] | |
---|---|---|---|
Gas | 950 | 9.6 | 0.09 |
Steam | 560 | 6.9 | 25 |
Growth temperature decreases along the circumferential direction and changes rapidly at approximately 90°. Reduced gas flow area enhances flow speed, which enlarges the convective heat transfer coefficient. At first, the growth temperature of the oxide scales increases fast as the difference of thermal conductivity between the metal and the oxide scales is large; see Figure
The growth temperature along the tube.
The oxide thickness along the tube.
The predicting results for oxide scale thickness are shown in Figure
The forecasting results.
0°, 30°, and 60°
90°, 120°, 150°, and 180°
Assume that the temperature drop of steam is 100°C while all other parameters remain the same. The stresses are calculated with (
The optimization progress of SVM parameters (Best
Radial stresses, axial stresses, and circumferential stresses in 0°, 90°, and 180° are shown in Figures
Forecasting results of radial stresses.
0° direction
90° direction
180° direction
Forecasting results of axial stress.
0° direction
90° direction
180° direction
Forecasting results of circumferential stress.
0° direction
90° direction
180° direction
The corresponding average errors and maximum errors are shown in Tables
The average forecasting errors for the stress.
0° | 90° | 180° | |
---|---|---|---|
Axial stress average error/[MPa] | 1.35 | 1.41 | 2.26 |
Circumferential stress average error/[MPa] | 0.40 | 0.50 | 0.66 |
Radial stress average error/[MPa] | 0.02 | 0.02 | 0.15 |
The maximum forecasting errors for the stress.
0° | 90° | 180° | |
---|---|---|---|
Axial stress maximum error/[MPa] | 76.85 | 40.99 | 24.28 |
Circumferential stress maximum error/[MPa] | 58.38 | 43.45 | 41.32 |
Radial stress maximum error/[MPa] | 4.39 | 4.46 | 1.99 |
The thickness and stress of oxide scales under uneven circumferential loading are calculated by finite volume method and finite element method, which are supplied as the samples. A soft sensor for oxide thickness and stress is proposed for the first time. An application shows that the soft sensor can give enough accurate results for oxide scale thickness and stress while the calculation time is greatly cut down. The soft sensor provides a convenient way to study oxide scale failure. In future, more operating parameters, tube diameters, and tube materials will be studied and incorporated into the predicting model.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors declare that there is no conflict of interests regarding the publication of this paper and acknowledge financial support from National Natural Science Foundation of China (51406077) and the Natural Science Foundation of Jiangsu Province, China (12KJB470008).